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[2601.22123] Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics
Summary
The paper introduces a novel framework for learning Hamiltonian Flow Maps that enables stable large-timestep updates in molecular dynamics simulations, addressing limitations of classical integrators.
Why It Matters
This research is significant as it enhances the efficiency of molecular dynamics simulations by allowing larger timesteps without compromising stability. This advancement can lead to faster simulations and broader applications in computational physics and chemistry, making it a valuable contribution to the field of machine learning in scientific computing.
Key Takeaways
- Introduces Hamiltonian Flow Maps for improved molecular dynamics.
- Allows for larger integration timesteps beyond classical limits.
- Trains on independent phase-space samples, avoiding trajectory generation.
- Maintains comparable costs for training and inference.
- Validated across diverse Hamiltonian systems, showing significant improvements.
Computer Science > Machine Learning arXiv:2601.22123 (cs) [Submitted on 29 Jan 2026 (v1), last revised 26 Feb 2026 (this version, v3)] Title:Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics Authors:Winfried Ripken, Michael Plainer, Gregor Lied, Thorben Frank, Oliver T. Unke, Stefan Chmiela, Frank Noé, Klaus-Robert Müller View a PDF of the paper titled Learning Hamiltonian Flow Maps: Mean Flow Consistency for Large-Timestep Molecular Dynamics, by Winfried Ripken and 7 other authors View PDF HTML (experimental) Abstract:Simulating the long-time evolution of Hamiltonian systems is limited by the small timesteps required for stable numerical integration. To overcome this constraint, we introduce a framework to learn Hamiltonian Flow Maps by predicting the mean phase-space evolution over a chosen time span, enabling stable large-timestep updates far beyond the stability limits of classical integrators. To this end, we impose a Mean Flow consistency condition for time-averaged Hamiltonian dynamics. Unlike prior approaches, this allows training on independent phase-space samples without access to future states, avoiding expensive trajectory generation. Validated across diverse Hamiltonian systems, our method in particular improves upon molecular dynamics simulations using machine-learned force fields (MLFF). Our models maintain comparable training and inference cost, but support significantly larger integration timesteps while trained di...
